Finite Group Databasebeta

← #387452

Subgroups — #387452

Order 512.

918 conjugacy classes of subgroups.

The subgroup lattice has 445 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2571C211yesmaximal, characteristic
2#21023C212yesmaximal
3#11355C212yesmaximal
4#11354C212yesmaximal
5#11204C212yesmaximal
6#10913C212yesmaximal
7#10858C212yesmaximal
8#10802C211yesmaximal, characteristic
9#10802C211yesmaximal, characteristic
10C2×#423C2212yes—
11C2×C4×M16C2212yes—
12#2571—22no—
13#2571—22no—
14#2571—22no—
15#2571—22no—
16C2×#400C414yes—
17C2×#389C412yes—
18C2×#389C2212yes—
19C2×#384C2211yescharacteristic
20C2×#382C412yes—
21C2×#382C2212yes—
22C2×C4×C4⋊C4C2211yescharacteristic
23C2×C4×C4⋊C4C2211yescharacteristic
24#1917—22no—
25#1917—22no—
26#1916—22no—
27#1916—22no—
28C2×#343C2212yes—
29C2×#343C2212yes—
30C2×#343C2212yes—
31C2×#343C2212yes—
32C2×#343C2211yescharacteristic
33C2×#343C2211yescharacteristic
34C2×#343C2211yescharacteristic
35C2×#343C2211yescharacteristic
36C2×#343C2212yes—
37C2×#343C2212yes—
38#1728C2212yes—
39#1728C2212yes—
40#1728C2212yes—
41#1728C2212yes—
42C22×M16C2312yes—
43C22×M16C2312yes—
44C22×M16C2312yes—
45C22×M16C2312yes—
46C22×C4⋊C4C2×C412yes—
47C22×C4⋊C4C2×C412yes—
48C22×C4⋊C4C2×C414yes—
49C22×C4⋊C4C2×C411yescharacteristic
50C22×C4⋊C4C2×C411yescharacteristic
51C22×C4⋊C4C2311yescharacteristic
52C22×C4⋊C4C2311yescharacteristic
53C22×C4⋊C4C2312yes—
54C22×C42C2×C412yes—
55C22×C42C2312yes—
56C22×C42C2311yescharacteristic
57#423—24no—
58#423—42no—
59C2×C4⋊C8—22no—
60C2×C4⋊C8—22no—
61C4×M16—24no—
62C4×M16—42no—
63C2×#97—22no—
64C2×C4×C8—22no—
65#400—24no—
66#400—24no—
67#400—24no—
68#400—24no—
69#389—24no—
70#389—22no—
71#389—22no—
72#389—22no—
73#389—22no—
74#389—22no—
75#389—22no—
76#384—22no—
77#384—22no—
78#382—24no—
79#382—22no—
80#382—22no—
81#382—22no—
82#382—22no—
83#382—22no—
84#382—22no—
85C4×C4⋊C4—22no—
86C4×C4⋊C4—22no—
87C4×C4⋊C4D412yes—
88C4×C4⋊C4D412yes—
89C4×C4⋊C4D412yes—
90C4×C4⋊C4D412yes—
91C2×#95C2×C412yes—
92C2×#95C2×C414yes—
93C2×#95C2×C414yes—
94C2×#95C2×C414yes—
95C2×#95C2×C412yes—
96#343—24no—
97#343—24no—
98#343—24no—
99#343—24no—
100#343—41no—
101#343—42no—
102#343—41no—
103#343—41no—
104#343—42no—
105#343—41no—
106#336—22no—
107#336—22no—
108#336—22no—
109#336—22no—
110#336—22no—
111#336—22no—
112#336—22no—
113#336—22no—
114C23×C4C22×C411yescharacteristic
115C23×C4C22×C414yes—
116C23×C4C22×C412yes—
117C23×C4C22×C412yes—
118C23×C4C22×C412yes—
119C23×C4C22×C411yescharacteristic
120C23×C4C22×C412yes—
121C23×C4C2411yescharacteristic
122C2×M16—22no—
123C2×M16—22no—
124C2×M16—22no—
125C2×M16—22no—
126C2×M16—22no—
127C2×M16—22no—
128C2×M16—22no—
129C2×M16—22no—
130C2×M16—22no—
131C2×M16—22no—
132C2×M16—22no—
133C2×M16—22no—
134C2×M16—22no—
135C2×M16—22no—
136C2×M16—22no—
137C2×M16—22no—
138C2×M16—22no—
139C2×M16—22no—
140C2×M16—22no—
141C2×M16—22no—
142C2×M16—22no—
143C2×M16—22no—
144C2×M16#4114yes—
145C2×M16#4114yes—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4—44no—
172C2×C4⋊C4—82no—
173C2×C4⋊C4—84no—
174C2×C4⋊C4C22⋊C412yes—
175C2×C4⋊C4C22⋊C412yes—
176C2×C4⋊C4C22⋊C411yescharacteristic
177C2×C4⋊C4C22⋊C411yescharacteristic
178C2×C4⋊C4C22⋊C411yescharacteristic
179C2×C4⋊C4C22⋊C411yescharacteristic
180C2×C42—22no—
181C2×C42—22no—
182C2×C42—22no—
183C2×C42—22no—
184C2×C42—21no—
185C2×C42—21no—
186C2×C42—22no—
187C2×C42—22no—
188C2×C42—22no—
189C2×C42—44no—
190C2×C42C2×D412yes—
191C2×C42C2×D412yes—
192C2×C42C2×D412yes—
193C2×C42C2×D412yes—
194C2×C42C2×D412yes—
195C2×C42C2×D412yes—
196C4⋊C8—44no—
197C4⋊C8—44no—
198#97—44no—
199C4×C8—44no—
200#95—24no—
201#95—24no—
202#95—24no—
203#95—24no—
204#95—24no—
205#95—24no—
206#95—24no—
207#95C22⋊C412yes—
208#95C22⋊C412yes—
209#95C22⋊C412yes—
210#95C22⋊C412yes—
211C24C23×C411yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—22no—
226C22×C4—24no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—44no—
240C22×C4—44no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4C2×C22⋊C412yes—
244C22×C4C2×C22⋊C412yes—
245C22×C4C2×C22⋊C412yes—
246C22×C4C2×C22⋊C412yes—
247C22×C4C2×C22⋊C412yes—
248C22×C4C2×C22⋊C411yescharacteristic
249C22×C4C2×C22⋊C411yescharacteristic
250C22×C4C22×D412yes—
251C22×C4C2×#4112yes—
252C22×C4C2×#4112yes—
253C22×C4H(5,𝔽2)11yescharacteristic
254C22×C4H(5,𝔽2)11yescharacteristic
255C22×C42−1+412yes—
256C22×C42−1+411yescharacteristic
257C22×C42−1+411yescharacteristic
258C22×C42−1+411yescharacteristic
259C22×C42−1+411yescharacteristic
260M16—24no—
261M16—24no—
262M16—24no—
263M16—24no—
264M16—42no—
265M16—42no—
266M16—42no—
267M16—42no—
268M16—42no—
269M16—42no—
270M16—42no—
271M16—42no—
272M16—42no—
273M16—42no—
274M16—42no—
275M16—42no—
276C2×C8—24no—
277C2×C8—24no—
278C2×C8—42no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—42no—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8—42no—
288C4⋊C4—24no—
289C4⋊C4—24no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C4⋊C4—44no—
295C4⋊C4—42no—
296C4⋊C4—42no—
297C4⋊C4—42no—
298C4⋊C4—42no—
299C4⋊C4—42no—
300C4⋊C4—42no—
301C4⋊C4—42no—
302C4⋊C4—42no—
303C4⋊C4—44no—
304C4⋊C4—84no—
305C4⋊C4—84no—
306C4⋊C4—84no—
307C42—22no—
308C42—22no—
309C42—22no—
310C42—22no—
311C42—22no—
312C42—22no—
313C42—22no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—22no—
318C42—22no—
319C42—44no—
320C42—44no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23C22×C22⋊C411yescharacteristic
326C23C4×#4111yescharacteristic
327C23C4×#4111yescharacteristic
328C23#51911yescharacteristic
329C23#51911yescharacteristic
330C23#52011yescharacteristic
331C23#52011yescharacteristic
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—22no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—44no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—82no—
365C2×C4—82no—
366C2×C4—82no—
367C2×C4—82no—
368C2×C4—82no—
369C2×C4—82no—
370C2×C4—84no—
371C2×C4—84no—
372C2×C4—82no—
373C2×C4—82no—
374C2×C4#41312yes—
375C2×C4#41312yes—
376C2×C4#53612yes—
377C2×C4#53612yes—
378C2×C4#53912yes—
379C2×C4#53912yes—
380C2×C4#54112yes—
381C2×C4#54112yes—
382C2×C4#54612yes—
383C2×C4#54712yes—
384C2×C4#54812yes—
385C2×C4#55012yes—
386C2×C4#55212yes—
387C2×C4#55212yes—
388C2×C4#56211yescharacteristic
389C2×C4#56311yescharacteristic
390C2×C4#56311yescharacteristic
391C2×C4#56411yescharacteristic
392C8—44no—
393C8—44no—
394C8—82no—
395C8—82no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22#231011yescharacteristic
409C22#233611yescharacteristic
410C22#233611yescharacteristic
411C22#233911yescharacteristic
412C22#234111yescharacteristic
413C22#237111yescharacteristic
414C22#238211yescharacteristic
415C22C2×#41311yescharacteristic
416C22C2×#41311yescharacteristic
417C22#288811yescharacteristic
418C22#288911yescharacteristic
419C4—22no—
420C4—22no—
421C4—42no—
422C4—42no—
423C4—42no—
424C4—42no—
425C4—42no—
426C4—82no—
427C4—84no—
428C4—82no—
429C4#269012yes—
430C4#269412yes—
431C4#271912yes—
432C4#272112yes—
433C2—21no—
434C2—21no—
435C2—21no—
436C2—21no—
437C2#1447411yescharacteristic
438C2#2183011yescharacteristic
439C2#2183211yescharacteristic
440C2#2248311yescharacteristic
441C2#2248411yescharacteristic
442C2#2253711yescharacteristic
443C2#2253911yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#25712
#210232
#113552
#113542
#112042
#109132
#108582
#108022